We have studied experimentally the nonequilibrium currents (NECs) induced by sweeping either the magnetic field B or the carrier density nS of a two-dimensional electron system (2DES). The gated 2DES resided in a modulation-doped GaAs/AlxGa1−xAs heterostructure and was integrated into a micromechanical cantilever. The NECs provoke a magnetic moment which we have detected via torque magnetometry down to 300 mK. Additional electrical leads allowed for simultaneous magnetotransport measurements. We find a hysteretic behavior of the NECs and a striking asymmetry of the corresponding magnetic moment around integer filling factors ν=hnS/eB. Surprisingly, the shape of the hysteresis loops is the same for sweeps of B or nS if plotted versus ν. In a certain parameter regime each NEC signal exhibits a characteristic slope which is found to depend only on the filling factor at large B or nS. Based on a model considering capacitive coupling between 2DES and gate we attribute the slopes to the conductance quantization of the quantum Hall effect. The NECs are found to be limited by the time-dependent buildup of the radial Hall field governed by the gate capacitance. These findings are in contrast to a floating 2DES without a gate where the breakdown of the quantum Hall effect was previously reported to limit the NECs. Our model also explains the observed shape and dependence on temperature as well as sweep rate. The in situ measurement of the longitudinal resistance allows us to directly correlate the magnetic behavior with both the magnetic field and temperature-dependent resistance of the 2DES.